-

    // input helper subroutine for converting from decimal to unary
    // step 1 "revconv": reverse the digits and convert them to zermelo
    // step 2 "unary": iterate through the digits and construct a unary number
    (@in @revconv
     [] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @unary
            [] [] [()] [$($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [0 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [() $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [1 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [(()) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [2 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [((())) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [3 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [(((()))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [4 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [((((())))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [5 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [(((((()))))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [6 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [((((((())))))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [7 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [(((((((()))))))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [8 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [((((((((())))))))) $($digit)*]
            $stuff
           )
    };
    (@in @revconv
     [9 $($tail:tt)*] [$($digit:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @revconv
            [$($tail)*] [(((((((((()))))))))) $($digit)*]
            $stuff
           )
    };

    // how step 2 works:
    // - $fullacc is the number being built up, $digitacc is used within digits (both are unary numbers)
    // - $pv is the place value counter, multiplied by 10 each iteration
    // - within a digit, count down the zermelo layers and inc $digitacc by $pv
    // - at the end of a digit, just add $digitacc to $fullacc (and multiply $pv by 10)
    (@in @unary
     $fullacc:tt $digitacc:tt $pv:tt []
     [[$head:tt $left:tt $right:tt] [$($other_stuff:tt)*]]
    ) => {
        bf!(@run $head
            [$fullacc $left $right]
            $($other_stuff)*
           )
    };
    (@in @unary
     [$($fullacc:tt)*] [$($digitacc:tt)*] [$($pv:tt)*] [() $($digits:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @unary
            [$($fullacc)* $($digitacc)*] [] [$($pv)* $($pv)* $($pv)* $($pv)* $($pv)*
                                             $($pv)* $($pv)* $($pv)* $($pv)* $($pv)*] [$($digits)*]
            $stuff
           )
    };
    (@in @unary
     $fullacc:tt [$($digitacc:tt)*] [$($pv:tt)*] [($digit:tt) $($digits:tt)*]
     $stuff:tt
    ) => {
        bf!(@in @unary
            $fullacc [$($digitacc)* $($pv)*] [$($pv)*] [$digit $($digits)*]
            $stuff
           )
    };